What is the optimal cheating strategy we can expect for this game? There are some strategies that can win Stern's single round zero-knowledge protocol with probability \(\frac{2}{3}\)  [1]} from which we can directly derive strategies for this game with 2 classical players that win wp. \(\frac{2}{3}\) . This means we have strategies for which the players win for 2 possible challenges for Bob but not for the third one.
